# Density Tree - What is the x axis?

I am looking at density trees

The intuition about the y-axis is clear: the tree indicates the modes which then merge at merge height:

$$m_p(x,y) = \sup{t: \exists C \in \textit{C} \quad s.t. \quad x,y \in C }$$

In terms of execution, everything goes through the use of a density estimator, as clearly described in the paper.

I am however not sure about what goes in the x-axis.

The fact that the x-axis ranges between 0 and 1 makes me suspect that the x-axis is somehow related with the distribution of the probability; but I am missing the details.

I have also checked the paper which is the original source of the picture above. There, the 1-dimensional case is somehow covered: . But I am still missing the details for n-dimensional cases, such as the Yingyang data.

• Try this earlier reference instead: Campello, Ricardo JGB, Davoud Moulavi, Arthur Zimek, and Joerg Sander (2013). "A framework for semi-supervised and unsupervised optimal extraction of clusters from hierarchies." Data Mining and Knowledge Discovery 27(3): 344-371. May 27 '17 at 15:37
• Thanks. Unfortunately the paper is not available for free and currently I do not have the budget for this. May 29 '17 at 8:38
• I can find it on Google... can't you?!? Because I can't subscribe to journals either. Fortunately, I can google pretty well... May 29 '17 at 16:35